Weak tautness and hyperconvexity in Hilbert spaces

The aim of this article "Weak tautness and hyperconvexity in Hilbert spaces" is to introduce the notions of weak tautness and hyperconvexity of a domain in a Banach space and to establish the relation between them. Moreover, some conditions under which a balanced domain in a Hilbert space and a Hartogs domain in a Banach space are hyperconvex are also given.